This activity is intended to supplement Geometry, Chapter 10, Lesson 4.
Time required: 30 minutes
Use technology to verify the circumference and area formulas for the circle.
In this activity, students explore the relationship between a circle’s circumference and its diameter. This will lead students to their own discovery of a value for pi.
This activity is designed to be used in a high school geometry clssroom.
Students should already be familiar with circles, diameter, circumference, and pi.
In this activity we will
Draw a circle
Measure the diameter of the circle
Measure the circumference of the circle
Calculate the ratio of the circumference to the diameter.
Press APPS. Move down to the Cabri Jr. APP and press ENTER. Press ENTER, or any key, to begin using the application.
Move the pencil until one endpoint of the diameter is flashing then press ENTER. Move to the other endpoint of the diameter and when it is flashing, press ENTER. Press + to see the measurement rounded to hundredths. The hand is active so you can move the measurement to a convenient location then press ENTER.
The Measurement tool is still active so now you can find the circumference of the circle. Move the pencil until the circle is flashing. Press ENTER then + to see the circumference rounded to hundredths. Move the hand until the measurement is in a convenient location. Press ENTER. Press CLEAR to turn off the measurement tool.
To explore this relationship with other circles, press CLEAR to turn off the Calculate tool. Move the arrow until the point which defined the circle’s radius or its center is flashing. Press ALPHA to activate the hand. Grab the point and move it to change the size of the circle.
To confirm that the ratio is still 3.14, repeat the Calculate procedure. (It is actually being recalculated each time the circle changes, but it is impossible to tell this since the number is unchanging.)